Physics · Electrostatics · chapter 2 of 14

Class 12 Physics Chapter 2: Electrostatic Potential and Capacitance case study question with answers

One case-based question of the kind the board asks: a passage and a figure, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks
A student models the field near a small charged sphere with a point charge +Q at its centre. She draws the equipotential surfaces for 900 V, 450 V and 300 V and finds them to be spheres of radii 10 cm, 20 cm and 30 cm, as in the figure. She now wants to locate other equipotential surfaces and to find how much work it takes to carry a small charge from one surface to another. Take 1/(4πε₀) = 9 × 10⁹ N m² C⁻² and the potential at infinity as zero.
900 V450 V300 V+Q102030 cm
Part 1 · 1 mark
The charge Q is
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Answer: (a) 10 nC

V = Q/(4πε₀r), so Q = Vr × 4πε₀ = 900 × 0.10/(9 × 10⁹) = 1.0 × 10⁻⁸ C = 10 nC.

Part 2 · 1 mark
The radius of the 600 V equipotential surface is
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Answer: (d) 15 cm

r = Q/(4πε₀V) = 9 × 10⁹ × 1.0 × 10⁻⁸/600 = 0.15 m. Since V ∝ 1/r, the 600 V surface is not midway between the 900 V and 300 V surfaces.

Part 3 · 2 marks
Find the work an external agent must do to carry a charge of +2.0 nC slowly from the 300 V surface to the 900 V surface. Does the answer depend on the path taken? Give a reason.
Answer and marking scheme

W = q(Vfinal − Vinitial) = 2.0 × 10⁻⁹ × (900 − 300) = 1.2 × 10⁻⁶ J. It does not depend on the path: the electrostatic force is conservative, so the work depends only on the end points.

  • W = qΔV = 1.2 × 10⁻⁶ J (1)
  • independent of path, since the force is conservative (1)
Or
Find the magnitude of the electric field at a point on the 450 V surface, and state its direction relative to that surface.
Answer and marking scheme

E = Q/(4πε₀r²) = 9 × 10⁹ × 1.0 × 10⁻⁸/(0.20)² = 2250 N C⁻¹ (equally, V/r = 450/0.20). It points radially outward, normal to the equipotential surface, towards lower potential.

  • E = 2250 N C⁻¹ (2.25 × 10³ N C⁻¹) (1)
  • radially outward, normal to the surface (1)
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